The Strange World of Quantum Mechanics 0521661048, 9780521661041

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This is an exceptionally accessible, accurate, and non-technical introduction to quantum mechanics. After briefly summarizing the differences between classical and quantum behavior, this engaging account considers the Stem-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstein-Podolsky-Rosen Paradox and Bell's theorem, Quantalinterference and the concept of amplitudes are introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in quantum computation and cryptography, discover the unexpected behavior of a quantal bouncing ball, and tackle the challenge of describing a particle with no position. Thoughtprovoking problems and suggestions for further reading are included. Suitable for use as a course text, The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure.

The Strange World of Quantum Mechanics Daniel F. Styer Oherlin College, Ohio

3 8888 03544843 4

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The Strange World of Quantum Mechanics This is an exceptionally accessible. accurate, and non-tcchnical introduction to quantum mechanics. After briefly summarizing the differences between classical and q u a n t u m b e h a v i o r this engaging account considers the Slern-Gerlach experiment and its implications, treats the concepts of probability, and then discusses the Einstcin-Podolsky-Rosen Paradox and Bell's theorem. Q u a n t a l interference and the concept of amplitudes arc introduced and the link revealed between probabilities and the interference of amplitudes. Quantal amplitude is employed to describe interference effects. Final chapters explore exciting new developments in q u a n t u m computation and cryptography, discover the unexpected behavior of a quantal bouncing balk and tackle the challenge of describing a particle with no position. Thought-provoking problems and suggestions for further reading are included. Suitable for use as a course text. The Strange World of Quantum Mechanics enables students to develop a genuine understanding of the domain of the very small. It will also appeal to general readers seeking intellectual adventure. is Professor of Physics at Oberlin College. A graduate of Swarthmore College and Cornell University, he has published technical research papers in Physical Review, Journal of Statistical Physics and the Proceedings of the Royal Society. Stycr is an associate editor of the American Journal of Physics, and his q u a n t u m mechanics software won the 1994 C o m p u t e r s in Physics Educational Software Contest. A m a n of lively intellect, Styers goal in life is to keep learning new things, and to that end he invests energy into presenting science to a general audience. T learn a lot through research and by teaching technical courses to physics majors,' says Stycr, %bul 1 learn even more by distilling the esscncc of physics ideas into a rigorously honest yet non-tcchnical presentation for a general audicnec. To reach this group, 1 cannot hide my ignorance behind a screen of mathematical formulas or technical jargon,' Professor Stycr enjoys running, backpacking, and rearing his two children as well as doing science. D A N STYLR

The Strange World of Quantum Mechanics Daniel F. Styer Oherlin College, Ohio

3 8888 03544843 4

CAMBRIDGE UNIVERSITY

PRESS

PUBLISHED

BY T H E P R E S S S Y N D I C A T E O F T H E U N I V E R S I T Y O F

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The Edinburgh Building. Cambridge CB2 2 R U , UK http://www.cup.cam.ac.uk 40 West 20th Street, New York, N Y 10011-4211, USA http://www.cup.org 10 Stamford Road, Oakleigh, Melbourne 3166, Australia Ruiz de Alarcon 13, 28014 Madrid, Spain © Daniel F. Styer 2000 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of C a m b r i d g e University Press First published 2000 Printed in the United K i n g d o m at the University Press, Cambridge Typeface Times 11 / 1 3 p t

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Library of Congress Cataloguing in Publication data Styer. Daniel F. T h e strange world of q u a n t u m mechanics / Daniel F. Styer. p. cm. Includes index. ISBN 0 521 66104 8. - ISBN 0 521 66780 1 (pbk.) 1. Q u a n t u m theory. 1. Title QC174.12.S879 1999 530.12-dc21 99-13559 C I P ISBN 0 521 66104 8 hardback ISBN 0 521 66780 1 paperback

Dedicated to two extraordinary teachers of quantum mechanics: John R. Boccio and N, David Mermin

1 here are more things in heaven and earth, 'Than are dreamt o f in your philosophy. T l a m I d I .v. 166

Horatio,

Contents

Preface

XI

1

1

Introduction

Classical mechanics describes how ordinary-sized things behave. mechanics describes how atomic-sized things behave.

Quantum

2

Classical Magnetic Needles 5 In classical mechanics, a compass needle behaves like a "magnetic a r r o w " that obeys certain rules. 3

The Stern-Cerlaeh Experiment 13 Kxperiments show that atomic-sized magnetic needles do not behave exactly like arrows. 4

The Conundrum of Projections; Repeated Measurements

21

In fact, atomic-sized magnetic needles can't behave like arrows at all! Repeated measurement experiments suggest that only probabilities, not certainties, can be predicted in q u a n t u m mechanics. 5

Probability

31

V

An understanding of probability is necessary lor q u a n t u m mechanics and important for day-lo-dav life, 6

The Einstein-Podolskv-Rosen Paradox

38

The probabilistic character of q u a n t u m mechanics, .suggested previously, is here proved. 7

Variations on a Theme bv Einstein Two more proofs, intellectual descendants of the Einstein-Podolsky argument. (This chapter is optional.) IX

49 Rosen

Contents

X

8

Optical Interference

57

Alomic-sizcd things don't behave in the familiar classical way. But how do they behave? Light, provides a clue, in that light from two sources can add up to produce not more light bul darkness. 9

Quanta! Interference

64

We design an apparatus with two routes through which an atom may pass from the input to the output. If the atom must pass through one route, then the probability of passage is If it must pass through the other route, then the probability of passage is i . Rut if it may pass through either route, then the probability of passage is ... zero! 10

Amplitudes

76

Quantal interference is described using an abstract entity called "amplitude". 11

Working with Amplitudes

86

Amplitude is represented mathematically by an arrow in a plane. Amplitude is associated with a process, not with a particle. 12

Two-Slit Inventions

94

Variations on the quantal interference experiment drive home the point that "the atom takes both routes". 13

Quantum Cryptography

98

Quantum mechanics invites deep thought about the nature of reality and the character of science. But on the practical level, it also allows the construction of an unbreakable code. (This chapter is optional.) 14

Quantum Mechanics of a liouncing Ball

103

The quantal rules for amplitudes, when applied to an ordinary-sized ball moving through space, give the same common-scnse result as classical mechanics — unless we trick the ball! 15

The Wavefunction

113

How does an atom behave when it has no position? How can humans visualize this behavior? Appendix A: A Brief History of Quantum Mechanics

119

Appendix B: Putting Weirdness to Work

133

Appendix C: Sources

138

Appendix D : General Questions

141

Appendix E: Bibliography

145

Appendix V: Skeleton Answers for Selected Problems

149

Index

151

Preface

This book presents the two ccntral conccpts of q u a n t u m mechanics in such a way that non-technical readers will learn how to work simple yet meaningful problems, as well as grasp the conceptual bizarreness of the quantal world, Those two central concepts arc: (1) The outcome of a n experiment cannot, in general, be predicted exactly; only the probabilities of the various outcomes can be found. (2) These probabilities arise through the interference of amplitudes. The book is based on a short course (only fourteen lectures) that I have presented to general-audience students at Oberiin College since 1989. and thus it is suitable for use as a course textbook. But it is also suitable for individual readers looking for intellectual adventure. The technical background needed to understand the book is limited to high school algebra and geometry. More important prerequisites arc an open mind, a willingness to question your ingrained notions, and a spirit of exploration. Like any adventure, reading this b o o k is not easy. But you will find it rewarding as well as challenging, and at the end you will possess a genuine understanding of the subject rather than a superficial gloss. How can one present a technical subject like q u a n t u m mechanics to a non-tcchnical audience? There are several possibilities. One is to emphasize the history of the subject and anecdotes a b o u t the founders of the field. Another is to describe the cultural climate, social pressures, and typical working conditions of a q u a n t u m physicist today. A third is to describe useful inventions, such as the laser and the transistor, that work through the action of q u a n t u m mechanics. A fourth is u> outline in general terms the mathematical machinery used by physicists in solving q u a n t u m mechanical problems. I find all four of these approaches unsatisfactory because they emphasize q u a n t u m physicists rather than q u a n t u m physics. This book uses instead a fifth approach, which emphasizes how nature behaves rather than how xi